Solve for $x$ and $y$ using elimination. ${5x-3y = -9}$ ${6x+3y = 42}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-3y$ and $3y$ cancel out. $11x = 33$ $\dfrac{11x}{{11}} = \dfrac{33}{{11}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {5x-3y = -9}\thinspace$ to find $y$ ${5}{(3)}{ - 3y = -9}$ $15-3y = -9$ $15{-15} - 3y = -9{-15}$ $-3y = -24$ $\dfrac{-3y}{{-3}} = \dfrac{-24}{{-3}}$ ${y = 8}$ You can also plug ${x = 3}$ into $\thinspace {6x+3y = 42}\thinspace$ and get the same answer for $y$ : ${6}{(3)}{ + 3y = 42}$ ${y = 8}$